Unit Hydrograph Theory Questions and Answers

Answer: C

The 1-h unit hydrograph peaks at 8 m³ s⁻¹ at 2 h.

The direct runoff hydrograph is 2 cm times the unit hydrograph plus 3 cm times the unit hydrograph lagged by 1 hour. Solve for the ordinates u in turn (direct runoff 0, 6, 25, 36, 26, 12, 0):

\[ \begin{aligned} 6 &= 2u_{1} \Rightarrow u_{1} = 3 \\ 25 &= 2u_{2} + 3u_{1} \Rightarrow u_{2} = 8 \\ 36 &= 2u_{3} + 3u_{2} \Rightarrow u_{3} = 6 \\ 26 &= 2u_{4} + 3u_{3} \Rightarrow u_{4} = 4 \end{aligned} \]

The ordinates 0, 3, 8, 6, 4, 0 give a peak of 8 at t = 2 h. Peaks at 1 h come from reading the first rise alone, and a peak of 7 or 9 does not satisfy the convolution.

Answer: C

The peak of the flood hydrograph is 280.5 m³/s.

The 6-hour unit hydrograph is the S-curve minus itself lagged by 6 hours: 0, 30, 60, 90, 72, 54, 36, 18, 0 m³/s at 0, 6, ..., 48 h, with a peak of 90 m³/s at 18 h.

\[ \begin{aligned} \text{loss} &= 0.25 \times 6 = 1.5\ \text{cm} \\ \text{excess} &= 4.5 - 1.5 = 3.0\ \text{cm} \\ \text{peak} &= 3 \times 90 + 10.5 = 280.5 \end{aligned} \]

270.0 is the peak direct runoff without the baseflow, and 259.5 subtracts the baseflow instead of adding it. 349.5 would need 339 m³/s of direct runoff, far more than 3 cm of rainfall excess can produce from a unit hydrograph whose peak is 90 m³/s per cm.

Answer: D

A unit hydrograph has one unit of direct run off.

A unit hydrograph is the direct runoff hydrograph produced by one unit depth (usually 1 cm) of effective rainfall falling uniformly over the catchment at a uniform rate for a specified duration. The area under it therefore equals one unit depth of direct runoff over the catchment.

The peak discharge and the time base are whatever the catchment produces; they are not one unit. The rainfall duration is specified (a 2-hour or 6-hour unit hydrograph, for instance) but is not fixed at one unit. Only the runoff volume is the defining unit.

Answer: D

It is the Unit hydrograph.

Sherman's unit hydrograph (1932) is the direct runoff hydrograph resulting from one unit (1 cm, or 1 mm) of excess rainfall falling uniformly over the watershed at a uniform rate during a specified duration. Assuming the watershed responds linearly, it represents the runoff process and is scaled and superposed to predict runoff from other storms.

A natural hydrograph is the observed one, a synthetic hydrograph is built from watershed characteristics where no records exist, and a dimensionless hydrograph expresses flow and time as ratios.